VIB - Simple Harmonic Motion

Simple Harmonic Motion

Simple Harmonic Motion occurs when objects oscillate back and forth and follow Hooke's Law. For an object to follow Hooke's Law, the force on the object must be proportional to the displacement from equilibrium and the force must be directed opposite to the direction of the displacement. The result is always a force that causes the object to accelerate back toward its original position. Please watch the following presentation that will discuss Simple Harmonic Motion. 

Simple Harmonic Motion Practice

We will now practice solving problems using the concepts you learned in the presentation. Make sure to show all your work when solving problems. The presentation will give you time to work through the problems, find a solution, and check your work.

Simple Harmonic Motion Self-Assessment

Now it's your turn. Complete the self-assessment questions to verify that you can apply the concepts of Simple Harmonic Motion.

  1. A 2.0 kg block is placed on a spring causing it to stretch 25 cm.
    1. What is the spring constant of the spring? 
    2. If the spring is now stretched 50 cm from equilibrium, what is the force of the spring? 
    3. What is the acceleration of the block at the maximum displacement?
    4. What is the period of oscillation? 
    5. What is the frequency of oscillation?

SOLUTIONS Links to an external site.

  1. A particle oscillates with simple harmonic motion along the x axis. Its position varies with time according to the equation  LaTeX: x\left(t\right)=4\cos\left(7t+0.8\right)x(t)=4cos(7t+0.8).
    1. What is the amplitude, frequency, and period of the motion of the particle? 
    2. What is the displacement of the particle at 1.5s?
    3. What is the velocity of the particle at 1.5s?
    4. What is the acceleration of the particle at 1.5s?

SOLUTIONS Links to an external site.

  1. A mass on a spring has its position given by the equation LaTeX: x=3m\cos\left(9t\right)x=3mcos(9t) 
    1. What is the maximum value for the magnitude of the object's velocity?
    2. How long will it take after the object starts moving for it to reach this maximum velocity?
    3. What is the maximum acceleration of the mass?
    4. At what time after the object is first released does the mass reach the maximum acceleration?

SOLUTIONS Links to an external site.

Simple Harmonic Motion Practice Problems

Download Simple Harmonic Motion Practice Problems Links to an external site. for more practice. 

Download solutions Links to an external site. to the practice problems. 

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